PRP Records

Probable Primes Top 10000

(293016 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
80012^335468-18629100986Enzo Doria05/2013
80022^335454-20961100982Enzo Doria06/2013
8003(2^335454+3258)/2100982Stefano Morozzi02/2021
800410^100978+61100979Lelio R Paula09/2016
800510^100978-156437100978Patrick De Geest11/2016
8006(2^335422+3114)/2100972Stefano Morozzi09/2020
8007(35*10^100970-89)/9100971Robert Price02/2022
8008(15*2^335417+1)/481100970Lelio R Paula12/2013
80092^335403-1859167100967Enzo Doria03/2016
801023599^18976+18976^23599100962Hans Havermann10/2018
80116*10^100958+43100959Robert Price07/2020
80129*2^335364-5100956Lelio R Paula08/2014
8013(7998^25867-1)/7997100955Serge Batalov06/2022
80142^335349+72287100951Enzo Doria04/2016
80152^335329+16095100945Lelio R Paula09/2016
8016232823#+233663100937Makoto Morimoto10/2017
8017(232823#+10141)/(10141*1674461)100927Makoto Morimoto06/2019
80182^335237-20893100917Enzo Doria06/2013
80192^335222-19337100912Enzo Doria05/2013
80202^335222-109985100912Enzo Doria04/2014
80212^335182-17237100900Enzo Doria05/2013
8022(2^335107+1634)/2100877Stefano Morozzi09/2020
80232^335043-16737100858Enzo Doria05/2013
8024(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
80252^335038-20633100857Enzo Doria06/2013
80262^335031+1873373100855Enzo Doria06/2016
802723489^19650+19650^23489100847Hans Havermann10/2018
80283^211354-8816100842Enzo Doria05/2014
80292^334984-112757100841Enzo Doria06/2014
8030(746*10^100827+1)/9100829Robert Price03/2020
803129451^2648+2648^29451100809Hans Havermann09/2018
803225583^8716+8716^25583100806Hans Havermann08/2018
80342^334857+48527100803Lelio R Paula08/2011
803312^93406+29100803Lelio R Paula10/2016
803528780^3179+3179^28780100796Hans Havermann09/2018
8036(5*2^334825+1)/47100792Lelio R Paula12/2013
8037(328^40063-1)/327100791Serge Batalov06/2022
80382^334809-13100788Lelio R Paula04/2011
8039(3552^28387-1)/3551100784Serge Batalov06/2022
8040(82*10^100780-1)/9100781Robert Price12/2014
804131395^1622+1622^31395100780Hans Havermann09/2018
8042(2^334779+47)/5100778Lelio R Paula12/2013
80432^334751+2049100771Lelio R Paula09/2016
804413^90443-98100749Lelio R Paula10/2016
8045(2^334674+3190)/2100747Stefano Morozzi09/2020
8046(2^334651+1050)/2100740Stefano Morozzi09/2020
8047(7*10^100737+71)/3100738Robert Price05/2018
8048(24737*2^334628+1)/3100737Lelio R Paula07/2014
804915^85639-28100720Lelio R Paula10/2016
805027068^5259+5259^27068100718Hans Havermann08/2018
80512^334562+577294575100711Lelio R Paula09/2016
80524*3^211077-5100710Lelio R Paula08/2014
80532^334524+145100702Lelio R Paula07/2009
8054(2^334451+714)/2100680Stefano Morozzi09/2020
805527648^4375+4375^27648100666Hans Havermann09/2018
8056(1017*2^334391-1)/3535100662Lelio R Paula05/2015
8057(2^334309+3122)/2100637Stefano Morozzi09/2020
80582^334294-113111100633Enzo Doria07/2014
805925581^8582+8582^25581100626Hans Havermann08/2018
80616^129308-17723100622Enzo Doria03/2013
8060(19*10^100627+287)/9/292157100622Alfred Reich11/2022
80626^129305+95100619Lelio R Paula10/2016
80632^334244-1167100618Lelio R Paula09/2016
8064(2^334233+3066)/2100614Stefano Morozzi09/2020
8065(76*10^100611+77)/9100612Robert Price10/2019
80667*10^100606-93100607Robert Price08/2020
8067(26*10^100566+49)/3100567Robert Price08/2019
8068(21*2^334050+1)/935100558Lelio R Paula12/2013
806924885^10984+10984^24885100555Hans Havermann07/2018
8070(1351^32119-1)/1350100551Serge Batalov06/2022
8071(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
8072(35*10^100542+1)/9100543Serge Batalov11/2010
807323578^18367+18367^23578100538Hans Havermann07/2018
807413^90251+24100535Lelio R Paula10/2016
80752^333963+789100533Lelio R Paula08/2011
80762^333919-1840087100520Enzo Doria06/2015
8077(2^333916+1698)/2100519Stefano Morozzi09/2020
80782^333911+72623100518Enzo Doria04/2016
807924605^12168+12168^24605100517Hans Havermann08/2018
808066*10^100502+7100504Robert Price07/2020
808118^80064-67100503Lelio R Paula10/2016
8082(13*10^100487+137)/3100488Robert Price06/2021
80835^143742-48100472Lelio R Paula10/2016
808424095^14784+14784^24095100472Hans Havermann08/2018
80852^333757-112123100471Enzo Doria06/2014
8086(7953^25759-1)/7952100470Serge Batalov06/2022
80877*10^100457-57100458Robert Price06/2020
808827358^4693+4693^27358100444Hans Havermann07/2018
80898*10^100439-51100440Robert Price08/2019
80902^333603-108861100425Enzo Doria03/2014
80919*7^118818-2100414Lelio R Paula11/2014
80922^333546-17097100408Enzo Doria05/2013
8093(19*10^100403+287)/9/3100403Alfred Reich11/2022
809417^81597+72100401Lelio R Paula10/2016
8095(3613^28219-1)/3612100396Serge Batalov06/2022
8096p(20559)#/2+8100384Robert Price01/2017
809711^96390-24100380Lelio R Paula10/2016
8098(2^333385+2730)/2100359Stefano Morozzi09/2020
80994832563059*2^333333+30029100353Donovan Johnson01/2008
810023565^18136+18136^23565100353Hans Havermann07/2018
81012^333354+763100350Lelio R Paula08/2011
8102(1608961*2^333333+1)/3100349Alex_soldier09/2022
8103(424517*2^333333+1)/5100349Alex_soldier09/2022
8104(887087*2^333333+1)/5100349Alex_soldier09/2022
8105(1159703*2^333333+1)/7100349Alex_soldier09/2022
8106(25*10^100343-67)/3100344Robert Price06/2019
81072^333289-109483100330Enzo Doria04/2014
81082^333240-2790209100316Enzo Doria03/2016
810923601^17798+17798^23601100314Hans Havermann05/2018
8111(2^333227-2^166614+1)/510031111/2006
81102^333225+719100311Lelio R Paula08/2011
81122^333221-2785333100310Enzo Doria10/2015
811376^53332-75100308Norbert Schneider02/2015
8114(29*10^100302+583)/9100303Robert Price06/2021
81156^128892-17573100298Enzo Doria03/2013
8116(47*10^100283-119)/9100284Robert Price05/2019
81172^333105-113215100275Enzo Doria07/2014
8118(31*2^333102+1)/2375100272Lelio R Paula11/2013
81194*10^100257-83100258Robert Price10/2018
812017^81476-74100253Lelio R Paula10/2016
812123392^19207+19207^23392100199Hans Havermann06/2018
8122(2^332830+750)/2100192Stefano Morozzi09/2020
8123(206*10^100189-17)/9100191Robert Price01/2020
812417^81417-16100180Theodore Burton11/2005
8125(2^332773+590)/2100175Stefano Morozzi09/2020
81262^332739-113215100165Enzo Doria07/2014
81272^332730-1865621100162Enzo Doria03/2016
812891^51127-2100160Lelio R Paula09/2013
812915^85159-32100155Lelio R Paula10/2016
81306^128661+97100118Lelio R Paula10/2016
813119^78285+40100108Lelio R Paula07/2016
81326^128640+5100102Lelio R Paula11/2014
813310^100095+89973100096Patrick De Geest10/2022
813410^100095-400001100095Robert Price09/2021
813510^100095-203693100095Patrick De Geest10/2022
813622779^22970-22970^22779100093Norbert Schneider08/2020
8137(2^332468+3130)/2100083Stefano Morozzi09/2020
8138(14*10^100075+61)/3100076Robert Price12/2018
8139(2^332435+3098)/2100073Stefano Morozzi09/2020
814028562^3189+3189^28562100072Hans Havermann05/2018
81416^128565-127100044Lelio R Paula08/2016
8142(2^332317+2106)/2100038Stefano Morozzi09/2020
81442^332309-133100035Lelio R Paula02/2011
81452^332307+731100035Lelio R Paula07/2011
8143937^33662-33662^937100035Norbert Schneider05/2023
81462^332301+12927100033Lelio R Paula04/2013
814723406^18781+18781^23406100031Hans Havermann04/2018
81482^332277-4573100026Yves Minet03/2019
814912^92684-13100023Lelio R Paula07/2016
815070^54207-54207^70100018Norbert Schneider04/2023
815178557*2^332193+55669100005Jorge Menendez04/2019
815278557*2^332192+72689100005Jorge Menendez04/2019
815310^100003+45799100004Stefano Morozzi04/2019
815410^100003+155461100004Stefano Morozzi04/2019
815510^100003+211389100004Stefano Morozzi04/2019
815610^100003+381027100004Stefano Morozzi04/2019
815710^100003+540703100004Stefano Morozzi04/2019
815810^100003+823977100004Stefano Morozzi04/2019
817010^100002+236023100003Stefano Morozzi05/2018
817110^100002+433741100003Stefano Morozzi05/2018
81592^332202+104659100003Stefano Morozzi04/2019
81602^332202+857539100003Stefano Morozzi04/2019
81612^332202+181773100003Stefano Morozzi04/2019
81622^332202+687543100003Stefano Morozzi04/2019
81632^332202+941595100003Stefano Morozzi04/2019
81642^332202+445813100003Stefano Morozzi04/2019
81652^332202+1599727100003Stefano Morozzi04/2019
81662^332202+1389567100003Stefano Morozzi04/2019
81672^332202+1206315100003Stefano Morozzi04/2019
81682^332202+1958647100003Stefano Morozzi04/2019
816910^100003-562857100003Patrick De Geest07/2019
8172(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
8173(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
817410^100002-249519100002Patrick De Geest07/2018
817510^100001+314199100002Patrick De Geest07/2018
819510^100000+3938473100001Robert Price05/2015
819610^100000+3979761100001Robert Price05/2015
819710^100000+4293973100001Robert Price09/2015
819210^100000+4858267100001Robert Price12/2015
819310^100000+5113299100001Robert Price02/2016
819410^100000+5169411100001Robert Price02/2016
818410^100000+5354043100001Robert Price05/2016
818510^100000+5717979100001Robert Price05/2016
818610^100000+6080631100001Robert Price07/2016
818710^100000+6308469100001Robert Price07/2016
818810^100000+6512023100001Robert Price08/2016
818910^100000+6596557100001Robert Price08/2016
819010^100000+7115409100001Robert Price10/2016
819110^100000+7235803100001Robert Price10/2016
819810^100000+7867333100001Robert Price12/2016
819910^100000+8743093100001Robert Price02/2017
820010^100000+8955391100001Robert Price03/2017
820110^100000+9180019100001Robert Price03/2017
820210^100000+9225987100001Robert Price04/2017
820310^100000+9265587100001Robert Price04/2017
820410^100000+9287049100001Robert Price04/2017
820510^100000+9425053100001Robert Price05/2017
820610^100000+9450769100001Robert Price05/2017
820710^100000+9528747100001Robert Smith05/2017
820810^100000+9548071100001Robert Price06/2017
820910^100000+10064287100001Robert Price08/2017
821010^100000+10229569100001Robert Price10/2017
817610^100000+11187931100001Robert Price03/2018
817710^100000+11264721100001Robert Price04/2018
817810^100000+11477661100001Robert Price05/2018
817910^100000+11644653100001Robert Price07/2018
818010^100001-431439100001Patrick De Geest07/2018
818110^100000+11769399100001Robert Price08/2018
818210^100000+11848159100001Robert Price08/2018
818310^100000+11863467100001Robert Price08/2018
821110^100000+11992051100001Robert Price09/2018
82122^332196-1-2*29696100001Matt Stath11/2018
821310^100000+12363957100001Robert Price11/2018
82142^332196+1+2*17152100001Matt Stath12/2018
821510^100000+12778033100001Robert Price02/2019
821610^100000+13581679100001Robert Price05/2019
821710^100000+13613199100001Robert Price05/2019
821810^100000+13752327100001Robert Price05/2019
821910^100000+14139243100001Robert Price06/2019
822010^100000+14151057100001Robert Price06/2019
822110^100000+14218923100001Robert Price06/2019
822210^100000+24543147100001Robert Price08/2021
822310^100000+24781659100001Robert Price08/2021
822410^100000+24906153100001Robert Price08/2021
822510^100000+25682679100001Robert Price10/2021
822610^100000+25905301100001Robert Price10/2021
822710^100000+25923967100001Robert Price10/2021
822810^100000+26061691100001Robert Price10/2021
822910^100000+26173351100001Robert Price11/2021
823010^100000+26673487100001Robert Price11/2021
823110^100000+26849359100001Robert Price12/2021
823210^100000+26893887100001Robert Price12/2021
823310^100000+26954551100001Robert Price12/2021
823410^100000+27024543100001Robert Price12/2021
823510^100000+27060877100001Robert Price12/2021
823610^100000+27617577100001Robert Price03/2022
823710^100000+27869671100001Robert Price03/2022
823810^100000+27956481100001Robert Price03/2022
823910^100000+28078261100001Robert Price03/2022
824010^100000+28150203100001Robert Price03/2022
824110^100000+28626021100001Robert Price05/2022
824210^100000+28649299100001Robert Price05/2022
824310^100000+29409799100001Robert Price06/2022
824410^100000+29415577100001Robert Price06/2022
824510^100000+29424201100001Robert Price06/2022
824610^100000+29610153100001Robert Price07/2022
824710^100000+30166789100001Robert Price07/2022
824810^100000+30338259100001Robert Price07/2022
824910^100000+30540031100001Robert Price07/2022
825010^100000+30635157100001Robert Price07/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 04 2023 08:38 (Time in France)

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